So I was studying the concept of rotational energy through a video, and the guy presented a problem,
It's like this:


"*Suppose a thin rod of mass M and length L/2 is hinged from one end. Then, it is released from rest (under gravity) from a horizontal position (making an angle of 0 degree from the horizontal). We have to find
"Angular Velocity of the rod when it makes a right angle with the horizontal (as shown)*"


[![enter image description here][1]][1]

As you can see, he solved this problem using mechanical energy conservation.

On the L.H.S. he took initial potential and kinetic energy; on the RHS he took final rotational kinetic and potential energy.

**Here lies my confusion. According to me, when the rod is rotating, the hinge reaction force, which is prependicular to the rod, also does work *(labeled as N1 in the image)*, then initially, the rod should also have potential energy due to these hinge forces *(or he should have included work done by these hinge forces in the equation*). Why, then, did he not include energy due to these forces in the equation?**

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On the right hand side of the equation, he wrote the term for Kinetic Energy as:

[![enter image description here][2]][2]

According to my conceptual clarity, this includes a change in kinetic energy due to gravity and hinge forces too.

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And the change in potential energy due to gravity, which is:

[![enter image description here][3]][3]


which is a change in potential energy due to gravity ONLY.


but there is no mention of these hinge forces. He then solves the equations to get an answer.

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**Why doesn't he account for work or energy changes caused by hinge forces?**

I believe that the work done by hinge forces should be included as a term on the left side of the equation.

A good explanation would help in clarifying my concepts.

  [1]: https://i.sstatic.net/C2m5f.png
  [2]: https://i.sstatic.net/MRqTB.png
  [3]: https://i.sstatic.net/J2sNU.png